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Source for wiki Infinity version 1

author

cowan

comment

ipnr

98.14.173.81

name

Infinity

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text

These are the R6RS examples involving `+inf.0` and `-inf.0` (already accounted for verbally in the "Implementation extensions" section of R7RS):

{{{
(complex? +inf.0)    => #t     ; infinities are real but not rational
(real? -inf.0)       => #t
(rational? -inf.0)   => #f
(integer? -inf.0)    => #f

(inexact? +inf.0)    => #t     ; infinities are inexact

(= +inf.0 +inf.0)    => #t     ; infinities are signed
(= -inf.0 +inf.0)    => #f
(= -inf.0 -inf.0)    => #t
(positive? +inf.0)   => #t
(negative? -inf.0)   => #t
(abs -inf.0)         => +inf.0

(finite? +inf.0)     => #f     ; infinities are infinite
(infinite? +inf.0)   => #t

                               ; infinities are maximal
(max +inf.0 x)       => +inf.0 where x is real
(min -inf.0 x)       => -inf.0 where x is real
(< -inf.0 x +inf.0)) => #t where x is real and finite
(> +inf.0 x -inf.0)) => #t where x is real and finite
(floor +inf.0)       => +inf.0
(ceiling -inf.0)     => -inf.0

                               ; infinities are sticky
(+ +inf.0 x)         => +inf.0 where x is real and finite
(+ -inf.0 x)         => -inf.0 where x is real and finite
(+ +inf.0 +inf.0)    => +inf.0

(+ +inf.0 -inf.0)    => +nan.0 ; sum of oppositely signed infinities is NaN
(- +inf.0 +inf.0)    => +nan.0

(* 5 +inf.0)         => +inf.0 ; infinities are sticky
(* -5 +inf.0)        => -inf.0
(* +inf.0 +inf.0)    => +inf.0
(* +inf.0 -inf.0)    => -inf.0

(/ 0.0)              => +inf.0 ; infinities are reciprocals of zero
(/ 1.0 0)            => +inf.0
(/ -1 0.0)           => -inf.0
(/ +inf.0)           => 0.0
(/ -inf.0)           => -0.0 if distinct from 0.0 

(rationalize +inf.0 3)      => +inf.0
(rationalize +inf.0 +inf.0) => +nan.0
(rationalize 3 +inf.0)      => 0.0

(exp +inf.0)         => +inf.0
(exp -inf.0)         => 0.0
(log +inf.0)         => +inf.0
(log 0.0)            => -inf.0
(log -inf.0)         => +inf.0+3.141592653589793i ; approximately
(atan -inf.0)        => -1.5707963267948965 ; approximately
(atan +inf.0)        => 1.5707963267948965 ; approximately

(sqrt +inf.0)        => +inf.0
(sqrt -inf.0)        => +inf.0i

(angle +inf.0)       => 0.0
(angle -inf.0)       => 3.141592653589793
(magnitude (make-rectangular x y)) => +inf.0 where x or y or both are infinite
}}}

time

2012-05-08 12:21:46